A company owns two dealerships, both of which sell cars and trucks. Dealership A sells a total of 164 cars and trucks. Dealership B sells twice as many cars and half as many trucks as Dealership A, and sells a total of 229 cars and trucks. (4 points)
a) An equation for the total cars and trucks for Dealership A: ____
b) An equation for the total cars and trucks for Dealership B:____
c) How many cars did Dealership A sell? ____
d) Considering that Dealership B sold half as many trucks as Dealership A, how many trucks did Dealership B sell?_____
a) An equation for the total cars and trucks for Dealership A:
Let's assume that the number of cars Dealership A sold is represented by 'x' and the number of trucks Dealership A sold is represented by 'y'.
From the given information, we know that Dealership A sold a total of 164 cars and trucks. So, the equation for the total cars and trucks for Dealership A can be written as:
x + y = 164
b) An equation for the total cars and trucks for Dealership B:
From the given information, we know that Dealership B sold twice as many cars and half as many trucks as Dealership A.
Let's assume that the number of cars Dealership B sold is represented by 'm' and the number of trucks Dealership B sold is represented by 'n'.
So, we can write the following equations:
m = 2x (Dealership B sold twice as many cars as Dealership A)
n = 0.5y (Dealership B sold half as many trucks as Dealership A)
To find the total number of cars and trucks for Dealership B, we can write the equation:
m + n = 229
c) How many cars did Dealership A sell?
From equation (a), we have x + y = 164
Since the question asks about the number of cars Dealership A sold, we need to isolate x.
x = 164 - y
d) Considering that Dealership B sold half as many trucks as Dealership A, how many trucks did Dealership B sell?
From equation (b), we have n = 0.5y
Since the question asks about the number of trucks Dealership B sold, we need to find the value of n when y = ? (from equation (c), we found that x = 164 - y, so y represents the number of trucks Dealership A sold).
Substituting y = 164 - y into the equation n = 0.5y, we get:
n = 0.5(164 - y)
We do not have enough information to determine the exact number of trucks Dealership B sold, as it depends on the value of y (the number of trucks Dealership A sold).
a) An equation for the total cars and trucks for Dealership A:
Let's assume the number of cars sold by Dealership A is "x" and the number of trucks sold by Dealership A is "y".
According to the given information, Dealership A sells a total of 164 cars and trucks. Therefore, we can write the equation as:
x + y = 164
b) An equation for the total cars and trucks for Dealership B:
Given that Dealership B sells twice as many cars and half as many trucks as Dealership A and sells a total of 229 cars and trucks.
Let's assume the number of cars sold by Dealership B is "a" and the number of trucks sold by Dealership B is "b".
According to the information, we can express the equations as:
a + b = 229
a = 2x (Twice as many cars as Dealership A)
b = 0.5y (Half as many trucks as Dealership A)
c) How many cars did Dealership A sell?
We know that x represents the number of cars sold by Dealership A. Therefore, the number of cars Dealership A sold is x.
d) Considering that Dealership B sold half as many trucks as Dealership A, how many trucks did Dealership B sell?
We know that y represents the number of trucks sold by Dealership A and b represents the number of trucks sold by Dealership B. Therefore, the number of trucks Dealership B sold is b.
a) The equation for the total cars and trucks for Dealership A can be represented as:
Cars (A) + Trucks (A) = 164
b) The equation for the total cars and trucks for Dealership B can be represented as:
Cars (B) + Trucks (B) = 229
c) To find out how many cars Dealership A sold, we need to solve the equation from part a).
From the equation:
Cars (A) + Trucks (A) = 164
We can see that the total sold by Dealership A is the sum of cars and trucks. However, we don't have information about the specific values.
d) To find out how many trucks Dealership B sold, we can consider that Dealership B sold half as many trucks as Dealership A. So, if we find the number of trucks sold by Dealership A, we can divide it by 2 to determine the number of trucks sold by Dealership B.
Since we don't know the exact number of trucks sold by Dealership A, we cannot provide the exact number of trucks sold by Dealership B.